I. To identify any pharmacokinetic interactions between ABT-888 and topotecan. (Phase I) II. To determine whether topotecan stimulates adenosine diphosphate (ADP)-ribose polymer formation in circulating peripheral blood mononuclear cells. (Phase I) III. To determine whether ABT-888 inhibits basal or topotecan-stimulated ADP-ribose polymer formation. (Phase I) IV. To assess differences in the toxicity and/or efficacy of this regimen based on BRCA 1/2 mutational status. (Phase II) V. To determine whether pretreatment tumor cell levels of topoisomerase I, poly ADP-ribose polymerase (PARP), BRCA1, BRCA2, XRCC1, tyrosyl-deoxyribonucleic acid (DNA) phosphodiesterase 1 (TDP1), P-glycoprotein or breast cancer resistance protein (BCRP) predict response to this regimen. (Phase II) VI. To identify, in an exploratory manner, any transcriptional profiles that may predict response to this regimen. (Phase II)